Question

What are all of the elements necessary to determine the equation of a line?

Answer 1

u would

Answer 2

if you determine equation of a line if 2 points are given

Answer 3

If two points are given you can calculate the slope by subtracting corresponding elements and taking the ratio, once you have that you can make an equation of the form
y=mx+b
Now sense you know m, and you have two values of y and x you can solve for b. Thus you can fully determine the equation of a line if you are given only two points.